A Laser-Chess Game

Leiserchess 2018 A Laser-Chess Game Charles E. Leiserson and the MIT 6.172 Staff Leiserchess (pronounced “LYE-sir-chess”) 2018 is a two-player laser-chess game similar to Laser Chess, Khet, and previous versions of Leiserchess. The teaching staff of the MIT class 6.172 Performance Engineering of Software Systems developed Leiserchess 2018 (henceforth just Leiserchess) for the term final project in Fall 2018. The students are given a working implementation of a program to play Leiserchess, and their job is to make it run as fast as possible and otherwise improve its playing ability. On the surface, Leiserchess is much simpler than Laser Chess or Khet in that there are only two kinds of pieces — Kings and Pawns — and all pieces move the same way. A deeper complexity arises from the dynamics of how pieces interact, however, because the Kings carry their own lasers to shoot at each other and at each other’s Pawns. The result is an entertaining and challenging game that involves both tactics and strategy. Pieces and Board Leiserchess is played on an 8x8 square board. Each player has one King and seven Pawns: Tangerine King Tangerine Pawn Lavender King Lavender Pawn The King contains a laser that can be activated to shoot out of its front. Each Pawn contains a mirror oriented at a 45-degree angle to the ranks and files of the board, which can deflect the beam of the laser from rank to file or vice versa. Opening Position Play begins with the following starting position: 1 Leiserchess 2018 ( ' & % $ # " ! ) * + , - . / 0 The starting position. Rules Tangerine moves first, and then play alternates between the two players. A player can only move his or her own pieces. All pieces in Leiserchess move the same, whether King or Pawn. A turn has two parts: moving, and firing the laser. A move is either a basic move or a swap move. Basic moves. For the first part of a turn, the player on move chooses a piece. For a basic move, the piece can either rotate by 90, 180, or 270 degrees, or it can move to an empty adjacent square in any of the eight compass directions while maintaining its orientation. A piece cannot both rotate and move as part of the same basic move. The following diagram shows a Pawn on a square and the 11 possible basic moves it can make: original position The 11 basic moves. 2 Leiserchess 2018 Swap moves. If an enemy piece occupies a square adjacent to the player’s piece, the two pieces swap positions, maintaining their orientations, and then the player’s piece can make an extra basic move. Here is an example: Initial position with Tangerine to move. Intermediate position after swap. Final position after extra basic move. Firing the laser. For the second part of a turn, the player fires the laser, which shoots out of the top of the King. The beam can safely bounce off the mirrored surfaces of Pawns, but if the laser “zaps” an opaque (nonmirrored) side of a piece, the zapped piece is removed from the board, no matter which player owns it. (Yes, you can zap your own Pawns and even commit suicide!) If a King is zapped, the game is over, and the player who owns the zapped King loses. After a player moves, he or she must always fire the laser, even if it is selfdestructive. For example, in the position shown below on the left, if Tangerine unwisely rotates the Pawn on !"/clockwise 90 degrees, as shown in the position on the right, it zaps its own King on #": ( ( ' ' & & % % $ $ # # " " ! ! ) * + , - . / 0 ) Tangerine to move. * + , - . / 0 Suicide! The Ko rule. To help ensure that the game makes progress, Leiserchess has a “Ko” rule similar to the Ko rule in the game of Go. The Leiserchess Ko rule says that a move is illegal if it “undoes” the opponent’s most recent move by returning the position to the position immediately prior to the current position. 3 Leiserchess 2018 Draws. A draw occurs (1) if there have been 50 moves by each side without a Pawn being zapped; (2) if the same position repeats itself three times with the same side on move; or (3) if the two players agree to a draw. Time control. As players become skilled, they tend to think longer. A chess clock (see http://en.wikipedia.org/wiki/Time_control) can be used to keep the pace up. Ideally, use a “delay” clock, such as a Fischer clock. Free chess-clock applications are available for many smart phones. Learning Leiserchess To learn the game, start by clearing the board of all Pawns, and play with just the two Kings, one in each corner of the board. You will discover that this endgame situation can always be won by one of the two players, who can force the enemy King to the edge and zap it. Playing this endgame will give you a feeling for the power of the laser-slinging Kings. Afterwards, go on to play normal games. Tactics. Despite the simplicity of the rules, Leiserchess has remarkably interesting tactics. For a King to zap the enemy King, it risks opening itself up to counterattack, and so shots must be artfully composed. For example, consider the following position with Tangerine to move: ( ' & % $ # " ! ) * + , - . / 0 Tangerine to move. Tangerine can zap the Lavender Pawn at $% by moving its Pawn on &' to (): 4 Leiserchess 2018 ( ' & % $ # " ! ) * + , - . / 0 Tangerine’s move zaps Lavender’s piece on $%. Doing so results in immediate disaster, however, as Lavender counters by moving its Lavender Pawn on *+ to &,, zapping the Tangerine King, and winning the game: ( ' & % $ # " ! ) * + , - . / 0 Lavender counterattacks and wins the game! The Pawns at (,, (), !), !-, and #-, which Tangerine used to reflect the laser to zap the Lavender Pawn at $%, are now used by Lavender in the reverse direction to zap the Tangerine King. Watch out for poison Pawns! This kind of tactic illustrates the “emergent complexity” inherent in Leiserchess, where the interaction of simple pieces engenders complex behavior. The “reverse- 5 Leiserchess 2018 path” nature of mirrors — “If you can see me, I can see you!” — produces a wealth of tactical issues. Strategy. Strategy is required for a player with a dominant position to prevail over the opponent. Without a thoughtful plan, the dominant player may not be able to engineer a zap. Although Leiserchess is a young game, some strategic elements have begun to emerge from games played so far: ● Keep some Pawns in the neighborhood of your own King. A “naked” King is generally easy to zap. ● Try to limit the mobility of the enemy King by threatening to attack the squares next to it. That is, be in a position to attack the enemy King should it move to an adjacent square. ● As the Kings move toward the center, a Pawn on the edge of the board can easily find itself unable to “cooperate” with other pieces in directing the path of the laser, rendering the Pawn next to useless. ● If the enemy King tries to “hunker down” by surrounding itself with its Pawns, you can invade with your Pawns to disrupt the enemy King’s defensive position. Recording Board Positions and Games Board positions can be recorded using a modified Forsyth-Edwards notation (FEN). From Tangerine’s point of view, list the pieces rank by rank, starting with rank 7 and ending with rank 0. Within each rank, describe the contents of each square from a to h as follows. Each piece is identified by a two-letter sequence describing the way it is facing, where upper case letters stand for Tangerine, and lower-case letters stand for Lavender. The Tangerine King is identified by NN, EE, SS, and WW, depending on whether it is facing north (toward the higher-numbered ranks), east (toward higher lettered files), south, or west. The Lavender King is similar, except lower-case letters are used. A Tangerine Pawn is identified by NE, SE, SW, and NW, depending on whether its mirror is facing northeast, southeast, southwest, or northwest, and similarly, using lower case, for the Lavender Pawns. The numbers 1 through 8 indicate consecutive empty squares, and a forward slash separates ranks. After the board description, the letter W or B (for White and Black, the traditional chess colors), depending on whether Tangerine has the next move in the position, or Lavender, respectively. For example, the opening position can be described with the following FEN string: ss7/3nwse3/2nwse4/1nwse3NW1/1se3NWSE1/4NWSE2/3NWSE3/7NN W Games can be recorded using the following simple notation: ! Leiserchess 2018 ● If a piece is rotated, write down the square holding the piece followed by either L for counterclockwise, R for a clockwise, or U for a 180-degree rotation, e.g., g2R. ● If a piece is moved to an adjacent empty square, write down the source square followed by the destination square, e.g., h3g4. ● If a piece swaps with an enemy piece, the two squares involved are recorded followed by the notation for the additional basic move taken by the piece: L, R, U, or the destination square. ● Record the outcome of the game as 1–0 (Tangerine wins), 0–1 (Lavender wins), or 1/2–1/2 (draw). Here is an example of a recorded game: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. g4g5 g5g4 g4L g4h5 f3e4 f2e3 h5g6 h0g0 e3e4 g0f0 d5c5b5 e2f2g2 e4d5R d5e6e7 e1d0 b5c4 d5R e6e7 e7e6 b3L b4R d5e4f5 f5g5 g5h4 c4R b3b2 d6d7 h4g3f2 c4b3 d7L b2b1 e4d3 d5c4c3 e2f3 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. g2g3 f3e4 e4d3c4 c4b5 h4g5 e4f3e2 e2f3g3 b5a4 b4b5a6 g5f6e5 g6g5f5 f0e1 e1e0 f5g6f6 f6f5 c2b2 d0c0R f3g3g2 d7L a7b7 e4d5d6 g2f3 e4f3 b7a7 b4a4b5 d7e7f6 a7L d6d7L d7c7 b4c3 b3c2 c2d1c0 b1a1 a1b2c1 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 0-1 e5e6 a1b1 b1R e0L b1b2c1 c1b2 e6U e6d5 f5e6 a1b1 e0f0 b1c1 d5L f0g1 g1h1 e6f5 c3c2 c1L d0R c1b2 b1a1 a1b2a3 a3R a7R c2U c7U c2d2 c7b7 d2e3 e3f3 f3g3 g3h3 !7 Leiserchess 2018